High-Quality-Factor Tunable Microdisk

ABSTRACT

An optical device includes a waveguide and a microdisk that is optically coupled to the waveguide. The gap between the microdisk and the waveguide is between 0.3 microns and 0.7 microns. The diameter of the microdisk is between 15 microns and 50 microns. The quality factor of the microdisk is at least 105. The microdisk is tuned optoelectrically or piezoelectrically.

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to microscale optical devices and, moreparticularly, to an optical device that includes a tunable microdiskresonator with a high quality factor.

High-quality-factor resonant optical devices such as Fabry-Perotcavities have been proposed as extremely effective tools for thedelicate manipulation and measurement of subtle quantum states (P Horaket al., “Possibility of single-atom detection on a chip”, Phys. Rev. Avol 67 p. 43806 (2003); W. von Klitzing et al., “Tunable whisperinggallery modes for spectroscopy and CQED experiments”, New J. Phys. Vol.3 p, 14 (2001)). If the quality factor of such a device is sufficientlyhigh, a single photon can interact many times with the same atom, ion ormolecule so that a significant interaction can be achieved. However, toachieve such strong coupling, the optical device must be kept onresonance with a frequency that is sufficiently close to the frequencyof the chosen quantum transition.

Tunable resonant microdisks have been used as filters and switches inoptical communication (Konstadin Djordjev et al., “Microdisk tunableresonant filters and switches”, IEEE Photonics Technology Letters vol.14 no. 6 pp. 828-830 (June 2002)).

A “microcavity” is, essentially, a microdisk turned inside-out.Integrated optical microcavities have been used in evanescent-wavespectroscopy (E. Krioukov et ala, “Integrated optical microcavities forenhanced evanescent-wave spectroscopy”. Optics Letters vol. 27 no. 17pp. 1504-1506 (September 2002)).

SUMMARY OF THE INVENTION

According to the present invention there is provided an optical deviceincluding: (a) a waveguide; and (b) a microdisk, optically coupled tothe waveguide, separated from the waveguide by a gap of between about0.3 microns and about 0.7 microns and having a diameter of between about15 microns and about 50 microns and a quality factor of at lea about10⁵.

The basic optical device of the present invention includes a waveguideand a microdisk that is optically coupled to the waveguide. The gapbetween the waveguide and the microdisk is between about 0.3 microns andabout 0.7 microns. The diameter of the microdisk is between about 15microns and about 50 microns, more preferably between about 15 micronsand about 30 microns, most preferably between about 15 microns and about20 microns. The quality factor of the microdisk is at least about 10⁵.

Preferably, the microdisk is substantially cylindrical. Alternatively,the microdisk is substantially toroidal, in which case the “diameter” ofthe microdisk is the outer diameter of the microdisk.

Preferably, the waveguide is tapered for mode matching with themicrodisk.

Preferably, the waveguide and the microdisk are fabricated on a commonsubstrate.

Preferably, the gap is at least about 0.5 microns and the quality factoris at least about 10⁶. Most preferably, the gap is about 0.7 microns andthe quality factor is at least about 10⁷.

Preferably, the optical device also includes a mechanism, such as anoptoelectric mechanism or a piezoelectric mechanism, for tuning themicrodisk.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is herein described, by way of example only, withreference to the accompanying drawings, wherein:

FIG. 1 is a schematic perspective view of a minimal optical device ofthe present invention;

FIG. 2 is a plan view of the device of FIG. 1;

FIG. 3 shows plots of calculated Q vs. D for several values of g;

FIG. 4 shows plots of calculated Q vs. D for two indices of refractionand two wavelengths at g=0.2 microns;

FIG. 5 shows plots of the relative changes in index of refraction and inD that provide a full spectral range scan, vs. D, for two indices ofrefraction.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is of a resonant-microdisk-based optical devicethat can be used for single-quantum-particle detection.

The principles and operation of a resonant-microdisk-based opticaldevice according to the present invention may be better understood withreference to the drawings and the accompanying description.

Referring now to the drawings, FIG. 1 is a schematic perspective view ofthe minimal optical device 10 of the present invention. Device 10includes a cylindrical microdisk 12 and a slab waveguide 14 fabricatedon a common substrate 16. Minimal device 10 is an integrated part of alarger system that includes several optical, electronic andmicromechanical devices all fabricated on a larger chip. Methods offabricating such chips are known in the art (T. J. Kippenberg et al.,“Fabrication and coupling to planar high-Q silica disk microcavities”,Appl. Phys Lett. Vol. 83 p. 797 (2003); D. K. Armani et al.,“Ultra-high-Q toroid microcavity on a chip”, Nature vol, 421p. 925(2003); V. Zwiller et al., “Fabrication and time-resolved studies ofvisible microdisk lasers”, J. Appl. Phys. Vol. 93 p. 2307 (2003)) and soneed not be recited herein.

FIG. 2 is a plan view of device 10, showing the geometric parameters ofdevice 10: the diameter D of microdisk 12 and the gap g betweenmicrodisk 12 and waveguide 14.

Waveguide 14 couples light into and out of microdisk 12. Adiabaticallytapered ends 18L and 18R of waveguide 14 are attached to optical fibers(not shown). In order to optimize power transfer between waveguide 14and a single-mode optical fiber, the mode overlap at the interfacebetween waveguide 14 and the optical fiber must be maximized. Forexample, typical cross-sectional dimensions of waveguide 14 are 9×9microns and 12×12 microns for the refractive index range of 1.454 to2.17 and 14×14 microns for a refractive index of 3.5, for wavelengthsaround 780 nm. Coupling efficiencies of 96% to 98% can be achieved. Forthe best mode matching with whispering gallery modes (WGM) in microdisk12, ends 18L and 18R need to taper inwards to a width of between 0.3microns and 1.2 microns.

Microdisk 12 is shown as a right-circular cylinder. Alternatively,microdisk 12 is a cylindrical torus, that supports almost the same WGMas a cylinder.

The optical properties of device 10 were modeled using finite differencetime domain (FDTD) (S. C. Hagness et al., “FDTD microcavity simulations:design and experimental realization of waveguide-coupled single-modering and whispering-gallery-mode disk resonators”, J. Lightwave Technol.Vol. 15 p. 2154 (1997)) and coupled mode theory (CMT) (D, R. Rowland andJ, D. Love., “Evanescent wave coupling of whispering gallery modes of adielectric cylinder”, IEEE Proceedings-J vol. 140 p. 177 (1993))methods. In most cases, the wavelength of the light was 780 nm, which isof interest as the wavelength of an electronic transition of Rubidium.

The objective of the modeling was to show the ability to obtain a highquality factor Q with relatively small disk sizes worthy of the name“microresonator”. In FIG. 3, the solid lines are plots of Q as afunction of D, obtained using CMT. Curves 20, 22, 24, 26 and 28 are,respectively, Q vs. D at gaps g of 0.1 microns, 0.3 microns. 0.5microns, 0.7 microns and ∞ (i.e., microdisk 12 not coupled to waveguide14), for a wavelength of 780 nm and an index of refraction of 1.454. Thefive solid dots were computed for g of 0.1 microns using FTDT, which iscomputationally much more expensive than CMT, to verify the accuracy ofthe CMT computations. The dotted line is a CMT computation for g about0.9 microns, a wavelength of 1550 nm and an index of refraction of1.444. The diamond is the corresponding measurement of Kippenberg et al.

To calculate Q for different values of D, the longitudinal index l ofthe WGM must be changed accordingly to keep the resonant wavelength near780 nm. The wavelength needed for optimal mode resonance can be achievedby choosing a precise value of D. Different materials have been used inthe prior art to fabricate microdisk resonators with refractive indicesranging from 1.444 up to 3.5. The values of 1.454 and 1.444 used in FIG.3 corresponds to fused silica at the respective wavelengths. Thefollowing table shows some sample CMT results. q is the radial index ofthe WGM.

Wave- D length Q Q (microns) l q (nm) (g = 0.3 microns) (g = 0.6microns) 30 167 1 778.73 1.55 × 10⁵ 8.44 × 10⁶ 30 166 1 783.27 1.47 ×10⁵ 8.05 × 10⁶ 30 159 2 780.04 1.83 × 10⁵ 8.85 × 10⁶ 15  81 1 780.417.66 × 10⁴ 3.82 × 10⁶ 45 253 1 780.15 2.66 × 10⁵ 1.40 × 10⁷

Values of Q also were computed using CMT and FDTD for other materials,with other refractive indices, for example AlGaAs/GaAs and SiN, forwhich tuning mechanisms have been reported, at a gap g of 0.2 microns.Some of these results are plotted in FIG. 4. The dashed curve in FIG. 4is for a wavelength of 780 nm and an index of refraction of 2.17, theindex of refraction of Si₃N₄ at that wavelength. The solid curve in FIG.4 is for a wavelength of 780 nm and an index of refraction of 1.454. Asin FIG. 3, the solid dots represent FDTD results corresponding to thesolid line. The dotted curve is for a wavelength of 1550 nm and an indexof refraction of 3.2. The diamonds represent measurements by Hagness etal.

In general, the resonance width of a microdisk is orders of magnitudenarrower than the microdisk's full spectral range (FSR). Therefore,coincidences between the transverse fundamental WGM of a microdisk andthe frequency of a quantum transition of interest are extremelyunlikely. To keep a WGM resonance near the wavelength of interest (notethat wavelength and frequency are equivalent in this context) either thediameter of the microdisk or the refractive index of the microdisk mustbe changed. In other words, the microdisk must be tuned. The tuningprocedure must be stable and reversible and the tuning range has to beof the same order of magnitude as the FSR. Under those conditions, aresonant mode close to the required quantum transition frequency alwayscan be found, even if the microdisk was fabricated with a mismatch indiameter or in refractive index. The tuning procedure also must be fastenough to compensate for temporal instabilities such as those arisingfrom temperature fluctuations of the chip.

Suitable tuning mechanisms include optoelectrical tuning andpiezoelectrical tuning. Such tuning affects the mode resonance viaΔv/v=Δn/n=ΔD/D, where v is the resonance mode frequency and n is theindex of refraction. To achieve full FSR tuning, Δv/v must beapproximately the reciprocal of the WGM longitudinal mode index l.Actually, because radial modes of several orders q can be used, thereare in fact several useable resonances within each FSR.

FIG. 5 shows the calculated Δn/n and ΔD/D needed to scan one fail FSR,vs. D, at a wavelength of 780 nm. The curve marked with triangles isΔn/n for an index of refraction of 2.17. The curve marked with diamondsis Δn/n for an index of refraction of 1.454. The curve marked with solidcircles is ΔD/D for an index of refraction of 2.17. The curve markedwith open circles is ΔD/D for an index of refraction of 1.454. The twolong arrows correspond to actual materials. The long arrow pointing tothe left shows experimentally obtained Δn/n for InP. The long arrowpointing to the right shows experimentally obtained ΔD/D for BaTiO₃.

In the case of optoelectrical tuning, the tuning is achieved by applyingto the microdisk a uniform electric field that tunes the opticalrefractive index of the microdisk, thereby changing the resonancewavelength. As shown in FIG. 1, the bottom of microdisk 12 is covered byan electrically conductive layer 30 and the top of microdisk 12 iscovered by an electrically conductive layer 32. A voltage is appliedacross layers 30 and 32 to create the necessary electric field. Forexample, crystalline materials usually have a relative index ofrefraction change of 0.01% to 1% for a field of 10⁵ volts per meter. Ifmicrodisk 12 is 5 microns thick, a voltage difference of 5 voltsprovides such an electric field across microdisk 5. FIG. 5 shows thatthe needed tuning can be achieved for microdisks 12 whose diameters Dare at least about 15 microns.

The piezoelectric effect also can be used to change the diameter of amicrodisk. In this case, the disk must be fabricated from a transparentpiezoelectric material. The voltage necessary for tuning is obtained asin the optoelectrical case using layers 30 and 32. Transparentpiezoelectric materials such as BaTiO₃ have a piezoelectric coefficienton the order of 10⁻¹⁰ meters per volt, which leads to ΔD/D around 0.003for electric fields of 3×10⁷ volts (150 volts across microdisk 12 ifmicrodisk 12 is 5 microns thick), FIG. 5 shows that in this case, Dgreater than or equal to about 30 microns enables a full FSR scan. Forboth optoelectric tuning of refractive index and piezoelectric tuning ofdisk diameter, using higher voltages and more exotic materials allowseven smaller disk diameters.

A comparison of FIGS. 3 and 5 shows that for microdisks 12 whosediameters D are in the tunability range, from about 15 microns to about50 microns, a quality factor of at least about 10⁵ can be attained,provided that the gap g between microdisk 12 and waveguide 14 is betweenabout 0.3 microns and about 0.7 microns. As seen in FIG. 3, higherquality factors than this have been achieved in the prior art but onlyfor larger gaps g and much larger diameters D. The highest qualityfactors that have been achieved in the diameter and gap ranges of thepresent invention, like the quality factors of Hagness et al that areshown in FIG. 4, are on the order of 10⁴.

While the invention has been described with respect to a limited numberof embodiments, it will be appreciated that many variationsmodifications and other applications of the invention may be made.

1. An optical device comprising: (a) a waveguide; and (b) a microdisk,optically coupled to said waveguide, separated from said waveguide by agap of between about 0.3 microns and about 0.7 microns and having adiameter of between about 15 microns and about 50 microns and a qualityfactor of at least about 10⁵.
 2. The optical device of claim 1, whereinsaid microdisk is substantially cylindrical.
 3. The optical device ofclaim 1, wherein said microdisk is substantially toroidal.
 4. Theoptical device of claim 1, wherein said waveguide is tapered for modematching with said microdisk.
 5. The optical device of claim 1, whereinsaid waveguide and said microdisk are fabricated on a common substrate.6. The optical device of claim 1, wherein said diameter is at most about30 microns.
 7. The optical device of claim 1, wherein said diameter isat most about 20 microns.
 8. The optical device of claim 1, wherein saidgap is at least about 0.3 microns and said quality factor is at leastabout 10⁶.
 9. The optical device of claim 1, wherein said gap is about0.7 microns and said quality factor is at least about 10⁷.
 10. Theoptical device of claim 1, further comprising: (c) a mechanism fortuning said microdisk.
 11. The optical device of claim 1, wherein saidmechanism is an optoelectric mechanism.
 12. The optical device of claim1, wherein said mechanism is a piezoelectric mechanism.